PHYS 1401 College Physics I CRN 55178 Khalid Bukhari HW 12 HOMEWORK PROBLEMS Chapter 12 THE LAWS OF THERMODYNAMICS PART A Hand in your answers in class on scantron on Monday 2010 Write your name class 1401 and HW 12 on the scantron 1 An ideal gas is maintained at a constant pressure of 70 0 kPa during an isobaric process while its volume decreases by 0 20 m3 What is the work done by the system on its environment a 14 kJ b 35 kJ c 14 kJ d 35 kJ e 72 kJ The work done by the system on the environment is Wenv P DV 70 0 103 Pa 0 20 m 3 14 103 J 14 kJ and c is the correct choice 2 A 2 0 mole ideal gas system is maintained at a constant volume of 4 0 liters If 100 J of thermal energy is transferred to the system what is the change in the internal energy of the system a 0 b 400 J c 70 J d 100 J e 0 100 J When volume is constant the work done on the gas is zero so the first law of thermodynamics gives the change in internal energy as DU Q W 100 J 0 100 J and d is the correct answer for this question 3 A monatomic ideal gas expands from 1 00 m3 to 2 50 m3 at a constant pressure of 2 00 X 5 10 Pa Find the change in the internal energy of the gas a 7 50 X 105 J b 1 05 X 106 J c 4 50 X 105 J d 3 00 X 105 J 3 For a monatomic ideal gas the internal energy is U 2 nRT and the change in internal 3 energy is DU 2 nR DT From the ideal gas law PV nRT observe that nR DT nRT fi nRT PffiV PVi When the pressure is constant Pfi P P this 3 3 reduces to DU 2 P V fi V 2 P DV so the change in internal energy for this gas is DU 32 2 00 105 Pa 1 50 m3 4 50 105 J making c the correct answer 4 An ideal gas drives a piston as it expands from 1 00 m3 to 2 00 m3 at a constant temperature of 850 K If there are 390 moles of gas in the piston how much work does the gas do in displacing the piston a 1 9 X 106 J b 2 5 X 106 J c 4 7 X 106 J d 2 1 X 105 J The work an ideal gas does on the environment during an isothermal expansion is Wenv nRT ln V fi V so for the given process Wenv 3 9 102 mol 8 31 J mol K 850 K ln 2 1 9 10 6 J and a is the correct choice 1 PHYS 1401 College Physics I CRN 55178 Khalid Bukhari HW 12 5 A diatomic ideal gas expands adiabatically from a volume of 1 00 m3 to a final volume of 3 50 m3 If the initial pressure is 1 00 X 105 Pa what is the final pressure a 6 62 X 104 Pa b 1 24 X 105 Pa c 3 54 X 104 Pa d 1 73 X 104 Pa For an adiabatic process PV g constant where g c p cv 1 4 for diatomic gases See Table 12 1 1 4 PV 1 4 i in the textbook Thus PffiV or the final pressure will be 1 4 1 4 Vi 1 00 m 3 5 Pfi P 1 00 10 Pa 1 73 10 4 Pa 3 50 m 3 V f 6 How much net work is done by the gas undergoing the cyclic process illustrated in Figure MCQ12 6 Choose the best estimate a 1 X 105 J b 2 X 105 J c 3 X 105 J d 4 X 105 J e 5 X 105 Pa In a cyclic process the net work done equals the area enclosed by the process curve in a PV diagram Thus Wnet 4 00 1 00 105 Pa 2 00 1 00 m 3 5 2 00 1 00 105 Pa 3 00 2 00 m 3 4 00 10 J and d is the correct answer 7 An engine does 15 kJ of work while rejecting 37 kJ to the cold reservoir What is the efficiency of the engine a 0 15 b 0 29 c 0 33 d 0 45 e 1 2 From conservation of energy the energy input to the engine must be Qh Weng Qc 15 kJ 37 kJ 52 kJ so the efficiency is Weng 15 kJ e 0 29 Qc 52 kJ or 29 and the correct choice is b 8 A refrigerator does 18 kJ of work while moving 115 kJ of thermal energy from inside the refrigerator What is its coefficient of performance a 3 4 b 2 8 c 8 9 d 6 4 e 5 2 The coefficient of performance of this refrigerator is Q 115 kJ COP c 6 4 which is choice d W 18 kJ 2 PHYS 1401 College Physics I CRN 55178 Khalid Bukhari HW 12 9 A steam turbine operates at a boiler temperature of 450 K and an exhaust temperature of 3 0 X 102 K What is the maximum theoretical efficiency of this system a 0 24 b 0 50 c 0 33 d 0 67 e 0 15 The maximum theoretical efficiency the Carnot efficiency of a device operating between absolute temperatures Tc Th is eC 1 Tc Th For the given steam turbine this is 3 0 102 K 0 33 450 K and c is the correct answer eC 1 or 33 10 A 1 00 kg block of ice at 0 C and 1 0 atm melts completely to water at 0 C Calculate the change of the entropy of the ice during the melting process For ice Lf 3 33 X 105 J kg a 3 340 J K b 2 170 J K c 3 340 J K d 1 220 J K e 1 220 J K At a pressure of 1 0 atm ice melts at absolute temperature TK 0 273 15 273 15 K The thermal energy this block of ice must absorb to fully melt is Qr mL f 1 00 kg 3 33 105 J kg 3 33 10 5 J so the change in entropy of the ice is Q 3 33 10 5 J DS r 1 22 103 J K 1 22 kJ K TK 273 15 K and d is the correct choice 11 If an ideal gas is compressed isothermally which of the following statements is true a Energy is transferred to the gas by heat b No work is done on the gas c The temperature of the gas increases d The internal energy of the gas remains constant e The pressure remains constant In an ideal gas the internal energy is directly proportional to …